y^{''}-4y^'+4y=sin(2x)

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{8} cos (2 x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = sin (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{8} cos (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{8} cos (2 x)

y^{^{''}} + 16 y = 32 sec (2 x)

(d^{2} - 2 d + 5) y = e^{x}

(d^{2} + 1) \cdot y = x \cdot cos (x)

(d^{2} - 4 d + 4) y = e^{2} x + sin^{2} (x)

(d^{2} - 1) \cdot y = x \cdot sinh (x)